r/LogicPuzzles • u/ErlandGadde • 6h ago
Recommendation Illogical Logic Quiz
The following question appeared on "1% Klubben" (The1% Club), a logic quiz show broadcast on Swedish television (SVT):
If the following is true:
1 = 5
2 = 27
3 = 125
4 = 1880
What is 5?
According to SVT, the correct answer is 1, with the explanation: Since 1 = 5, 5 = 1.
I understand the idea is to think outside the box, but as the question is worded, it is misleading, and there is more than one answer.
If you think along the lines of the people who designed SVT's puzzle, there is at least one other correct answer: 5, because 5 = 5, after all.
The “box” is, of course, the assumption that there is a pattern in the numbers to the right of the equals signs that you are supposed to identify. But that requires you not to interpret the equals signs literally, treating the expressions as a numbered list rather than a sequence of equations.
Yet the puzzle designers evidently intend the equals signs to mean exactly what they normally mean: equality, and nothing else. But in that case, the equations are false: 1 is not equal to 5, and so on. Strictly speaking, this means that any number (and indeed anything at all) is a correct answer, since an implication is always true if its antecedent is false: “If 1 = 5, etc., then 5 = x” is true whatever x may be.
But perhaps the right-hand sides need not be interpreted as ordinary numbers in base 10, or perhaps not even as numbers at all? Could some interpretation make the equations true? Possibly. But however you interpret the equations, 5 = 5, and therefore there is at least one correct answer besides 1, namely 5.
(Episode 2, at 48:33, on SVT Play)